Gun Ownership and Suicides
Gun ownership has been shown to be highly correlated with suicides. There is little debate over this. Research has also shown that there is little substitution to other methods, guns make suicide easy and other methods involve significantly more pain and/or planning. Many suicide attempts are transient impulses linked to life events (estimates vary from about a third on up); the increased rate of suicide in households with firearms acts through this channel. Waiting periods have been shown to be very effective in reducing gun suicide rates. These findings hold in both US only and international comparisons.
Gun Ownership and Homicide
The link between gun ownership and homicide is also well established, though there remains well founded efforts to make this controversial and there remain many questions regarding the strength of the relationship and the influence of confounding factors. There are some observations that deserve to be made about these studies.
First of all, international comparisons show a stronger relationship than do studies that look solely within the US, this is likely due to the difficulty of controlling the flow of arms within a free trade area where gun control laws differ relative to controlling this flow across international boundaries.
There are also questions regarding calculating rates of firearms ownership. This does make any single study problematic (which is one reason I am not linking to specific studies, no one study is very compelling but look up gun ownership and homicide rates in Google Scholar and you an read the abstracts yourself) but the association between gun ownership and homicide is robust to virtually all methodologies used, though the strength of the relationship differs.
Finally, there are likely other factors at work aside from gun control, most notably the drug trade and how organized crime functions in a given country. These, and other factors, do make the data noisy, but the robustness of the link to different methodologies as well as to within country as well as international comparisons makes the link pretty definitive, even if it remains controversial.
Gun Ownership and Other Crimes
There is little relationship between gun ownership and any crime aside from homicide. Few studies find a statistically significant relationship, those that do tend towards finding an association between gun ownership and an increased rate of violent crimes that cause bodily harm, rapes and assaults, and a decrease in violent crime aimed at property, burglaries and robberies. But these associations are very weak and differ across studies. There is no evidence of a measurable deterrence effect at the population level, and studies that have tried to look at reports of guns deterring crimes tend to find that instances are vastly exaggerated relative to actual formal reports, that often defensive use of guns results from the escalation of heated arguments that likely would not have escalated without the presence of firearms (or resulted in simple fisticuffs), and property crimes that resulted in justifiable homicide, often involving insured property.
The major outlier was a well publicized paper by Lott and Mustard which found a strong association between concealed carry laws and reductions in violent crime. This paper has been widely, and repeatedly, discredited. It is criticized for a biased selection of years, other sets yield different results, for using county level data to assess state wide changes, for failing to use standardized robustness checks, and for other academic flaws including misrepresentation of the data. Most notably, no one has been able to replicate the study and its findings run contrary to other methodologies to assess gun control and parts of this study contradict well known facts about crime. The refutation of this paper does not appear to be partisan, there are academic gun control advocates who also claim strong connections between firearm ownership and non-homicide crimes, these papers have been exposed as deeply flawed as well and are also widely viewed as discredited. Since none of these papers have received anything like the strong promotion that the Lott study has received by motivated interests I will refrain from naming names.
Gun Control and Homicide/Suicide Prevention
Most studies find that gun control does successfully impact the incidence of gun crimes. There is a large degree of variability in how effective various approaches are, with local controls being relatively ineffective relative to national laws, but the direction always appears to be in the expected direction, no matter how weak the relationship.
Generally speaking, these laws do seem to show diminishing returns. There appears to be rather sharp drop-offs in homicides as gun control tightens initially, but there does not appear to be much additional reduction once European norms are met. The near full gun bans instituted by Britain and Australia have been argued to have some effect, but with such a low homicide rate it is difficult to tell if there was any real decline or if it was just noise in a small sample size. Swiss levels of gun control seem to have already achieved the bulk of what is possible. There is little reason to think that gun control laws should progress beyond this.
It is worth pointing out separately that despite the undue attention they receive, assault weapons are rarely used in crime. Estimates I have seen are generally in the low single digits, there is little reason to believe that an assault weapons ban would have a statistically significant impact on homicides.
Policies of more merit would be restrictions on concealed carry (there seems to be no significant negative impact of may-issue laws, with the exception of the discredited Lott study, shall-issue laws are usually found to be problematic), mandatory firearm licensing, closing loopholes on firearms sale (and moving towards a Swiss system where all firearms purchases must be recorded, including between individuals), and limiting the sale of firearms (such as a one gun per month policy). Given the high rate of gun ownership in the US, and the large pool of illegal guns, I tend to think a gun buy-back program targeting unregistered firearms will also be necessary after better policies are put into effect.
TV, Video Games, and Homicides
The role of violent media in violent crime is frequently brought up alongside the role of guns. The evidence here is far more mixed than the link between homicides and guns.
There are a few relevant issues to sort out here. First, psychological studies do show a heightened aggressive response in those exposed to violent media. There is considerable dispute over this, but it seems to be the case that the majority of researchers feel there is some association, though it would also appear that more recent research is pushing back against these conclusions. In any case, it is a much messier debate than that regarding guns and homicide.
What is extremely unclear is whether there are any population level effects on criminal violent crime. We can say with a great degree of certainty that if there is an effect, it is far smaller than the impact of gun ownership. There is also no visible relationship at the international level between video game purchasing and homicides, as there is with gun ownership (the Incidental Economist has had three good posts on video games and violence over the past few days).
A third issue is the impact of TV and video games generally on social behavior. Here we have a more likely association. TV viewing (I don't know about video games) has been shown to be linked to a decline in positive social behaviors that generate social capital. There does seem to be a link between strong communities and crime more generally. However, this is not a link between violence and crime, watching Downtown Abbey has just as much impact as watching Natural Born Killers. What matters is how much media consumption is displacing social activities. It does also need to be said that TV watching is not the sole culprit here, and my generation and younger have been showing a rebound in social capital relative to the boomers (possibly, but by no means certainly, correlated with declining crime rates in the US).
Other Factors and Violent Crime
The last thing I want to point out is that neither gun possession or TV consumption are the strongest drivers of violent crime (though gun possession does appear to be the strongest factor with regards to homicide in international comparisons). Sociological factors tend to dominate, chief among them being a disadvantaged minority (this is not just specific to blacks in the US but is visible in other minorities in other countries). Access to health care, poverty, good schools, and especially inequality are more important than either guns or TV for explaining the variance in rates of crime across societies. But since broad-based social reform is even less likely in the US than is gun control, this is relevant only for putting things in perspective.
To conclude, we need a few things to have a rational gun debate in the US. First of all, we need to realize that there is a distinction to be made between homicide/suicide and violent crime more generally, firearm possession is not associated with other violent crimes. Secondly,we need to agree what constitutes evidence, I am constantly frustrated by the insistence in the media that some fool's opinion is of equal value in being reported as well defined studies with transparent results and methodologies. Third, we need to admit the role that powerful, concentrated interests play in distorting this conversation.
I would point specifically to this post from the Incidental Economist bringing this fact to us:
To ensure that the CDC and its grantees got the message, the following language was added to the final  appropriation: “none of the funds made available for injury prevention and control at the Centers for Disease Control and Prevention may be used to advocate or promote gun control.”
Precisely what was or was not permitted under the clause was unclear. But no federal employee was willing to risk his or her career or the agency’s funding to find out. Extramural support for firearm injury prevention research quickly dried up. Even today, 17 years after this legislative action, the CDC’s website lacks specific links to information about preventing firearm-related violence.
When other agencies funded high-quality research, similar action was taken. In 2009, Branas et al published the results of a case-control study that examined whether carrying a gun increases or decreases the risk of firearm assault. In contrast to earlier research, this particular study was funded by the National Institute on Alcohol Abuse and Alcoholism. Two years later, Congress extended the restrictive language it had previously applied to the CDC to all Department of Health and Human Services agencies, including the National Institutes of Health.
We can't have an informed, rational conversation about this when there are powerful lobbies interested in preventing us from having this conversation. Despite the political assertions to the contrary, this is not an area where there is any kind of real controversy over the data. The results are as one-sided as the global warming or smoking and cancer debates were. To have this debate, we need to put the real interests of gun owners vs. the real data on the consequences of that gun ownership. Deciding that interests of gun owners outweigh the costs would be a perfectly legitimate democratic decision, weighing false consequences with no evidence vs. established, real-world observational evidence is not a debate that leads to legitimate democratic decision making.